MinT - Best Known (88−41, 88, s)-Nets in Base 16

Best Known (88−41, 88, s)-Nets in Base 16

(88−41, 88, 520)-Net over F₁₆ — Constructive and digital

Digital (47, 88, 520)-net over F₁₆, using

trace code for nets [i] based on digital (3, 44, 260)-net over F₂₅₆, using
- net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(88−41, 88, 642)-Net over F₁₆ — Digital

Digital (47, 88, 642)-net over F₁₆, using

2 times m-reduction [i] based on digital (47, 90, 642)-net over F₁₆, using
- trace code for nets [i] based on digital (2, 45, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(88−41, 88, 95738)-Net in Base 16 — Upper bound on s

There is no (47, 88, 95739)-net in base 16, because

1 times m-reduction [i] would yield (47, 87, 95739)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 573 404463 739084 866471 670450 441829 037630 231120 202326 083199 674787 563466 715612 051046 968039 455497 981516 394826 > 16⁸⁷ [i]